| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.2.8.56a2.817 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.818 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.819 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.820 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.821 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.822 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.823 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.824 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.825 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.826 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.827 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.828 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.829 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.830 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.831 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.832 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.833 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.834 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.835 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.836 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.837 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.838 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.839 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.840 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.841 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.842 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.843 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.844 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.845 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.846 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.847 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(4 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.848 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.849 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.850 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.851 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.852 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.853 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.854 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.855 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.856 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.857 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.858 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.859 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.860 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.861 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.862 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.863 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.864 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + \left(12 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.961 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(12 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.962 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.C_2\wr C_4$ (as 16T1698) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
